Derivatives worksheet with answers

Free printable Derivatives worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyx = −2

Let f(x) = −3x3 − 2x2 + 4x + 3. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x3 − 2x2 + 4x + 3x = −2
f′(−2) =
2.Easy
xyx = −2

Let f(x) = 5x4 − x2 + 6x − 8. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 5x4 − x2 + 6x − 8x = −2
f′(−2) =
3.Medium
xyx = 3

Let f(x) = ln(2x2 + 4). Find f′(3).

f(x) = ln(2x2 + 4)x = 3
f′(3) =
4.Medium
xyx = −1

Let f(x) = (4x + 5)4. Find f′(−1).

f(x) = (4x + 5)4x = −1
f′(−1) =
5.Hard
xyx = 2

The tangent line to f(x) = −x2 − 3x + 3 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 3x + 3x = 2
b =
6.Hard
xyx = 1

The tangent line to f(x) = 2x2 + 2x + 1 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 2x + 1x = 1
b =

Answer key

  1. 1. f′(−2) = −24
  2. 2. f′(−2) = −150
  3. 3. f′(3) = 0.5455
  4. 4. f′(−1) = 16
  5. 5. b = 7
  6. 6. b = −1

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